Mathematics
Grade 10
15 min
Add and subtract mixed numbers: word problems
Add and subtract mixed numbers: word problems
What you'll learn
- Identify the necessary information and operation(s) needed to solve word problems involving addition and subtraction of mixed numbers with 80% accuracy.
- Solve word problems involving addition and subtraction of mixed numbers with unlike denominators by rewriting them with common denominators and finding the correct answer at least 3 out of 4 times.
- Explain the steps taken to solve a word problem involving addition or subtraction of mixed numbers, including renaming fractions, in a clear and logical manner to a partner.
- Apply addition and subtraction of mixed numbers to solve real-world problems presented in word problems, demonstrating understanding by obtaining correct solutions in at least 75% of the problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate word problems involving congruent figures into mathematical expressions with mixed numbers.
Calculate the perimeter of polygons whose side lengths are given as mixed numbers.
Determine an unknown side length of a figure by applying the properties of congruence and mixed number subtraction.
Solve multi-step problems requiring both addition and subtraction of mixed numbers in a geometric context.
Verify calculations by converting mixed numbers to improper fractions and performing the operations.
Interpret geometric diagrams to formulate equations involving mixed numbers.
How does a structural engineer calculate the total length of steel needed for two congruent triangular trusses if the side lengths are 8 1/4 ft, 15 7/8 ft, and 15 7/8 ft? 🏗️
Whil...
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Key Concepts & Vocabulary
TermDefinitionExample
Mixed NumberA number consisting of a whole number and a proper fraction.The length of a side of a triangle is 5 3/4 inches.
Improper FractionA fraction in which the numerator is greater than or equal to the denominator. Mixed numbers are often converted to improper fractions for easier calculation.The mixed number 5 3/4 is equivalent to the improper fraction 23/4.
Congruent FiguresFigures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.If Triangle ABC ≅ Triangle XYZ, then the length of side AB is equal to the length of side XY.
Corresponding PartsThe sides or angles of congruent figures that are in the same relative position.In two congruent pentagons, the shortest side of the first pentagon corresponds to the short...
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Core Formulas
Addition of Mixed Numbers
A \frac{b}{c} + D \frac{e}{f} = (A + D) + (\frac{b}{c} + \frac{e}{f})
Add the whole numbers and the fractions separately. If the resulting fraction is improper, convert it to a mixed number and add its whole part to the total.
Subtraction of Mixed Numbers (Regrouping)
If \frac{b}{c} < \frac{e}{f}, then A \frac{b}{c} = (A-1) + \frac{b+c}{c}
When subtracting, if the first fraction is smaller than the second, you must 'borrow' or 'regroup' 1 from the whole number. The borrowed 1 is expressed as a fraction (c/c) and added to the existing fraction before subtracting.
Conversion to Improper Fractions
A \frac{b}{c} = \frac{A \times c + b}{c}
An alternative method for both addition and subtraction is to convert all mixed numbe...
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Challenging
Three congruent equilateral triangles, each with a side length of 4 1/3 inches, are placed in a row so that they share sides. What is the perimeter of the resulting trapezoid shape?
A.13 inches
B.26 inches
C.21 2/3 inches
D.17 1/3 inches
Challenging
Two congruent polygons, P1 and P2, each have a perimeter of X. When they are joined along a corresponding side of length Y, the new perimeter is 50 1/2. If the length of the joined side Y is 5 3/4, what is the perimeter of one of the original polygons (X)?
A.31
B.28
C.36 1/4
D.44 3/4
Challenging
Given ΔABC ≅ ΔDEF. The perimeter of ΔABC is 30 units. Side AB = 9 1/3 units and side BC = 12 1/2 units. What is the length of side DF?
A.9 1/3 units
B.12 1/2 units
C.21 5/6 units
D.8 1/6 units
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What grade level is "Add and subtract mixed numbers: word problems"?
Add and subtract mixed numbers: word problems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract mixed numbers: word problems?
You'll be able to: Identify the necessary information and operation(s) needed to solve word problems involving addition and subtraction of mixed numbers with 80% accuracy; Solve word problems involving addition and subtraction of mixed numbers….
Is "Add and subtract mixed numbers: word problems" free to practice?
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How many practice questions are included with Add and subtract mixed numbers: word problems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.